I'm not quite sure if I understand what you mean but as far as I think I understood is that you put a pen on to a jack or your computer and it snapped then you pushed it further in to the jack? If I got that right then I suggest getting a screw and a screwdriver (if wanted) and screw the pen out of the jack. I had this problem but it wasn't a pen it was a headphone jack it snapped in the phone's headphone jack! Hope this works if this isn't the problem your having please explain to me what your problem is again?

Samsung Chromebooks (Basic, Plus, and Pro) have styluses that go into the body of the machine, like the old Palm Pilots and other PDAs, with a little clicky tip on one end, like a regular pen, that likes to break off. If that happens, the stylus gets stuck in the machine, like if you put half a stylus into one of the old pdas...

Those Styluses aren't super easy to get out of those chromebooks, especially when they break like that.... @slinkliechan is on to something, try taking an M4 or an M5 screw (whichever is VERY slightly larger than the body of the stylus, so it'll only bite the inside), drive it into the body of the stylus. and very carefully pull it out of the chromebook. Then, replace that stylus, they're like $25usd right now on most parts sources.